Our goal is to $\textit{efficiently}$ discover a compact set of temporal
logic rules to explain irregular events of interest. We introduce a
neural-symbolic rule induction framework within the temporal point process
model. The negative log-likelihood is the loss that guides the learning, where
the explanatory logic rules and their weights are learned end-to-end in a
$\textit{differentiable}$ way. Specifically, predicates and logic rules are
represented as $\textit{vector embeddings}$, where the predicate embeddings are
fixed and the rule embeddings are trained via gradient descent to obtain the
most appropriate compositional representations of the predicate embeddings. To
make the rule learning process more efficient and flexible, we adopt a
$\textit{sequential covering algorithm}$, which progressively adds rules to the
model and removes the event sequences that have been explained until all event
sequences have been covered. All the found rules will be fed back to the models
for a final rule embedding and weight refinement. Our approach showcases
notable efficiency and accuracy across synthetic and real datasets, surpassing
state-of-the-art baselines by a wide margin in terms of efficiency.

我们引入了一个神经符号规则归纳框架，该框架通过时序点过程模型高效地发现一个紧凑的时间逻辑规则集合来解释感兴趣的不规则事件。我们采用了矢量嵌入来表示谓词和逻辑规则，并通过梯度下降训练逻辑规则嵌入以获得谓词嵌入的最适合的组合表示。为了使规则学习过程更高效和灵活，我们采用了顺序覆盖算法，该算法逐步将规则添加到模型中，并移除已解释的事件序列，直到所有事件序列都被覆盖。在合成和真实数据集中，我们的方法表现出显著的效率和准确性，以较大的优势超过了现有技术基准的效率。